MX0016

divisor_pair_index_map_lookup

Alpha v34 independently verified · alpha_closed; checked-use authorized; not Stable

At supplied genuine row and bounded column coordinates, the actual beta code stores their product.

Current library: Alpha v34, 4,223 checked-use theorems; Stable remains 432. Historical first admissions, original proof editions, and non-admitted aliases are preserved.

Exact expanded first-order arithmetic statement

forall V L r s i d e. (((~((V)=0)) /\ (forall dpi_index_dpi_lookup_map dpi_row_dpi_lookup_map dpi_column_dpi_lookup_map. (exists pvs_gap_dpi_lookup_mapwindow. pvs_gap_dpi_lookup_mapwindow + S (dpi_index_dpi_lookup_map) = (L)) -> (exists pvs_gap_dpi_lookup_mapremainder. pvs_gap_dpi_lookup_mapremainder + S (dpi_column_dpi_lookup_map) = (V)) -> (dpi_index_dpi_lookup_map)=(V)*(dpi_row_dpi_lookup_map)+(dpi_column_dpi_lookup_map) -> (((exists ff_h_pvs_dpi_lookup_mapvalue. ff_h_pvs_dpi_lookup_mapvalue + S ((dpi_row_dpi_lookup_map)*(dpi_column_dpi_lookup_map)) = S ((S (dpi_index_dpi_lookup_map)) * s)) /\ exists ff_q_pvs_dpi_lookup_mapvalue. r = ff_q_pvs_dpi_lookup_mapvalue * S ((S (dpi_index_dpi_lookup_map)) * s) + ((dpi_row_dpi_lookup_map)*(dpi_column_dpi_lookup_map))))))) -> (exists pvs_gap_dpi_lookup_index. pvs_gap_dpi_lookup_index + S (i) = (L)) -> (exists pvs_gap_dpi_lookup_column. pvs_gap_dpi_lookup_column + S (e) = (V)) -> i=V*d+e -> (((exists ff_h_pvs_dpi_lookup_result. ff_h_pvs_dpi_lookup_result + S (d*e) = S ((S (i)) * s)) /\ exists ff_q_pvs_dpi_lookup_result. r = ff_q_pvs_dpi_lookup_result * S ((S (i)) * s) + (d*e)))

Constructive proof overview

Generated structural guide

At supplied genuine row and bounded column coordinates, the actual beta code stores their product.

The unchanged tactic script uses 0 declared prerequisites and contains 19 exact native proof lines.

Alpha v34 checked-use · first admitted v32 · independently kernel and Lean verified; not Stable

Proof neighborhood

Direct dependencies

none

Direct dependents

Formal native tactic body

Dependencies are introduced as named hypotheses before line 1. Local theorem links identify exact declared prerequisites. This exact body belongs to a complete independently kernel-checked constructive proof bundle and has Alpha checked-use authority; it does not imply Stable membership.

Read the argument

Proof checkpoints

19 script commands · 4 reading checkpoints · 0 local claims

This is a reading aid, not a new proof or a proof-tree certificate. Checkpoint groups are consecutive commands, not inferred branch boundaries. Every step links to the preserved script.

01Fix variables and assumptionsL1–10

Work with arbitrary variables or the premises of the current implication.

  1. L1
    intro V
  2. L2
    intro L
  3. L3
    intro r
  4. L4
    intro s
  5. L5
    intro i
  6. L6
    intro d
  7. L7
    intro e
  8. L8
    intro hm
  9. L9
    intro hi
  10. L10
    intro he
02Fix variables and assumptionsL11–11

Work with arbitrary variables or the premises of the current implication.

  1. L11
    intro heq
03Separate the logical casesL12–12

Follow the explicit conjunction, disjunction, witness, or contradiction step recorded below.

  1. L12
    cases hm
04Use earlier factsL13–19

Instantiate or apply named facts and discharge the corresponding proof obligations.

  1. L13
    specialize hm_right (i)
  2. L14
    specialize hm_right (d)
  3. L15
    specialize hm_right (e)
  4. L16
    apply hm_right
  5. L17
    exact hi
  6. L18
    exact he
  7. L19
    exact heq

Library-wide reading audit

Original exact command ledger · 19 lines
  1. 0001intro V
  2. 0002intro L
  3. 0003intro r
  4. 0004intro s
  5. 0005intro i
  6. 0006intro d
  7. 0007intro e
  8. 0008intro hm
  9. 0009intro hi
  10. 0010intro he
  11. 0011intro heq
  12. 0012cases hm
  13. 0013specialize hm_right (i)
  14. 0014specialize hm_right (d)
  15. 0015specialize hm_right (e)
  16. 0016apply hm_right
  17. 0017exact hi
  18. 0018exact he
  19. 0019exact heq